بررسي و تحليل برهان خلف در دو نظام منطقي قديم و جديد

A Survey and Analysis of the Indirect Proof in Ancient and Modern Logic

In modern logic, the logical implication between premises and the conclusion in any proof, and also the implication between negation of conclusion and its contradiction in indirect proofs are material implications whereas in ancient logic they have Lozomi relations. Besides, in indirect proofs, after assuming this Lozomi relation it is assumed that the conclusion itself is accidentally (in way of Ettefaghieh) conditioned to its negation and this relation is considered as the basis for the indirect proof. According to this research, this relation is firstly neither the basis of the indirect proof, for it is unnecessary, nor there is any need to assume it, and secondly the reason given for it is unacceptable. It will be also shown that the domain of application of the indirect proof in ancient logic has been overexteneded. In addition, the application of the indirect proof in different formal structures is a factor of consistency and completeness of the structure, and so it has no use in multi-valued formal structures because it is based on the law of excluded middle.